This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. There have been many single nucleotide polymorphism-based tests suggested for association analysis in a case-control design. The possible evidence for association comprises three types of information: differences between cases and controls in allele frequencies, in parameters for Hardy Weinberg disequilibrium (HWD) and in parameters for linkage disequilibrium (LD). However, the parameters for LD require knowledge about phase, which is usually unknown, making the LD contrast test without modification infeasible in practice. Methods for handling phase uncertainty are: (1) the most probable haplotype pair for each individual can be considered as the true phase;(2) a weighted average of haplotypes can be used;(3) we can consider the composite LD, which does not require any information about phase. We compare these methods to handle phase uncertainty in terms of validity and efficiency, and the effect on them of HWD in the population, at the same time confirming results for the three types of information. When the LD between markers is high, the LD contrast test that uses a weighted average of haplotypes or the most probable haplotypes to calculate the LD is recommended, but otherwise the LD contrast test that uses the composite LD is recommended. In another study, we examine two single-marker tests and four two-marker tests. The true association models are derived and they allow us to understand why a model with only a linear term will generally fit well for a SNP in weak LD with a causal SNP, whatever the disease model, but not for a SNP in high LD with a non-additive disease SNP. We investigate the power of the association tests using real LD parameters from chromosome 11 in the HapMap CEU population data. Among the single-marker tests, the allelic test has on average the most power in the case of an additive disease, but for dominant, recessive, and heterozygote disadvantage diseases, the genotypic test has the most power. Among the four two-marker tests, the Allelic-LD contrast test, which incorporates linear terms for two markers and their interaction term, provides the most reliable power overall for the cases studied. Therefore, our result supports incorporating an interaction term as well as linear terms in multi-marker tests.